Find a nine-digit number such that the first digit is divisible by one,
the first two digits are divisible by 2, the first three digits are
divisible by 3,..., the whole nine-digit number is divisible by nine.

I'm having real problems trying to divide using a non place system,
like with Roman numerals. The concept of using letters rather than
numbers is confusing me. Can you please give me an example of a
division calculation?

What kinds of numbers have exactly 3 divisors? Do bigger numbers
necessarily have more divisors? Is there a way to figure out how many
divisors 1,000,000 has without actually listing and counting them?...

My students think PEMDAS means that all addition should be done before
any subtraction is done. How can I show and convince them that they
need to do both operations at the same time working from left to right?